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A Process Calculus with Finitary Comprehended Terms

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Abstract

We introduce the notion of an ACP process algebra and the notion of a meadow enriched ACP process algebra. The former notion originates from the models of the axiom system ACP. The latter notion is a simple generalization of the former notion to processes in which data are involved, the mathematical structure of data being a meadow. Moreover, for all associative operators from the signature of meadow enriched ACP process algebras that are not of an auxiliary nature, we introduce variable-binding operators as generalizations. These variable-binding operators, which give rise to comprehended terms, have the property that they can always be eliminated. Thus, we obtain a process calculus whose terms can be interpreted in all meadow enriched ACP process algebras. Use of the variable-binding operators can have a major impact on the size of terms.

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Notes

  1. We write \(\mathbb{N}^{+}\) for the set \(\mathbb{N}\setminus \{ 0 \}\).

  2. The name comprehended term originates from the name comprehended expression introduced in [27].

  3. We write ≡ for syntactic identity.

  4. We use the convention that, whenever we write log2(n) in a context requiring a natural number, ⌈log2(n)⌉ is implicitly meant.

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Acknowledgements

We thank an anonymous referee for carefully reading a preliminary version of this paper, for pointing out some slips made in it, and for suggesting improvements of the presentation.

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  1. Informatics Institute, Faculty of Science, University of Amsterdam, Science Park 904, 1098 XH, Amsterdam, The Netherlands

    J. A. Bergstra & C. A. Middelburg

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  1. J. A. Bergstra
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  2. C. A. Middelburg
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Correspondence to C. A. Middelburg.

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Bergstra, J.A., Middelburg, C.A. A Process Calculus with Finitary Comprehended Terms. Theory Comput Syst 53, 645–668 (2013). https://doi.org/10.1007/s00224-013-9468-x

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